Bounding the smallest robustly control invariant sets in networks with discrete disturbances and controls

Abstract

This paper is concerned with the reliability of logistics networks, specifically the problem of guaranteeing their robustness to uncertainties in operating conditions while maintaining economical storage costs. Indeed, we investigate logistics networks in a setup where both the disturbances and control actions take their values in prescribed finite alphabet sets, we revisit recently derived bounds on the 'l1' norm of the smallest invariant hyperbox sets, we show that the existing bounds are conservative, and we propose a tighter new lower bound.